The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics QCD , and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the t...

A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation (Dk+Yfcrn~JQ bmDm)f = 0 , where each bm is a complex number, D is the Dirac operator in R" , and f is defined on a domain in R" and takes values in a complex Clifford algebra. Some basic properties for the solutions to this equation, arising from the integral formula, are described, including an approximatio...

In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems...

In this article, we described basic properties of Riemann integral on functions from R into Real Banach Space. We proved mainly the linearity of integral operator about the integral of continuous functions on closed interval of the set of real numbers. These theorems were based on the article [10] and we referred to the former articles about Riemann integral. We applied definitions and theorems...

(a) The curves z(s) and z(s, t) were not required to be simple curves. This made the task of approximating them with continuously differentiable curves very easy. (b) The Cauchy integral theorem also holds if the function z(s) describing the curve C is merely piecewise continuously differentiable. For in this case we carry out the integration by parts in (6) over each subinterval on which zs(s)...

It is a well known fact that transfer functions of scattering conservative systems and impedance conservative system are the analytic contractive function in the unit disk and functions with positive real part on the upper half plane, respectively. In this case, the interplay between the transfer functions is via the Moebius transformation. In the system representation the interplay is by the s...

Abstract The definition of a Green’s function Cauchy–Dirichlet problem for the hyperbolic equation in quarter plane is given. Its existence and uniqueness have been proven. Representation It shown that can be represented by Riemann–Green function.